Abstract
Spectral risk measures provide the framework to formulate the risk aversion of a firm specifically for each quantile of the loss distribution of a portfolio. More precisely the risk aversion is codified in a weight function, weighting each quantile. Since the basic coherent building blocks of spectral risk measures are expected shortfall measures, the most intuitive approach comes from combinations of those. For investment decisions the marginal risk or the capital allocation is the sensible approach. Since spectral risk measures are coherent there exists also a sensible capital allocation based on the notion of derivatives or more in the light of the coherency approach as an expectation under a generalized maximal scenario.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Acerbi, C. (2002). Spectral measures of risk: A coherent representation of subjective risk aversion. Journal of Banking and Finance, 26, 1505–1518.
Acerbi, C., & Tasche, D. (2002). On the coherence of expected shortfall. Journal of Banking and Finance, 26, 1487–1503.
Artzner, P., Delbaen, F., Eber, J.-M., & Heath, D. (1997). Thinking coherently. RISK, 68–71.
Artzner, P., Delbaen, F., Eber, J.-M., & Heath, D. (1999). Coherent measures of risk. Mathematical Finance, 9, 203–228.
Bluhmn C., Overbeck, L., Wagner, C. (2002). An introduction to credit risk modeling. Boca Raton: CRC Press/Chapman & Hall.
Crouhy, M., Galai, D., Mark, R. (1999). A comparative analysis of current credit risk models. Journal of Banking and Finance, 24.
Delbaen, F. (2000). Coherent risk measures. Lecture notes, Scuola Normale Superiore di Pisa.
Denault, M. s. (2001). Coherent allocation of risk capital. Journal of Risk, 4, 1.
Kalkbrener, M. (2002). An axiomatic approach to capital allocation. Technical Document, Deutsche Bank AG, Frankfurt.
Kalkbrener, M., Lotter, H. & Overbeck, L. (2004). Sensible and efficient capital allocation. Risk.
Kurth, A., & Tasche, D. (2003). Contributions to credit risk. Risk, 84–88.
Overbeck, L.(2000). Allocation of economic capital in loan portfolios. In Stahl/Härdle (Eds.), Proceedings “Measuring Risk in Complex Stochastic Systems”. Lecture Notes in Statistics, 1999. Berlin: Springer.
Overbeck, L., & Stahl. G. (2003). Stochastic essentials for the risk management of credit portfolios. Kredit und Kapital, 1.
Overbeck, L. (2004). Spectral Capital Allocation. London: RISK Books.
Rockafellar, R. T., & Uryasev, S. (2000). Optimization of conditional value-at-risk. Journal of Risk, 2, 21–41.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer-Verlag GmbH Germany
About this chapter
Cite this chapter
Overbeck, L., Sokolova, M. (2017). Risk Measurement with Spectral Capital Allocation. In: Härdle, W., Chen, CH., Overbeck, L. (eds) Applied Quantitative Finance. Statistics and Computing. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-54486-0_6
Download citation
DOI: https://doi.org/10.1007/978-3-662-54486-0_6
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-54485-3
Online ISBN: 978-3-662-54486-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)